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DTOC3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DTOC3
* Problem :
* *********
* This is a discrete time optimal control (DTOC) problem.
* The system has N time periods, 1 control variable and 2 state variables.
* The problem is convex.
* Sources: problem 3 in
* T.F. Coleman and A. Liao,
* "An Efficient Trust Region Method for Unconstrained Discret-Time Optimal
* Control Problems",
* Tech. Report, ctc93tr144, Advanced Computing Research Institute,
* Cornell University, 1992.
* D.P. Bertsekas,
* "Projected Newton methods for optimization problems with simple
* constraints",
* SIAM J. Control and Optimization 20, pp. 221-246, 1982.
* SIF input: Ph. Toint, August 1993
* classification QLR2-AN-V-V
* Problem variants: they are identified by the value of the parameter N.
* The problem has 3N-1 variables (of which 2 are fixed),
* and 2(N-1) constraints
*IE N 10 $-PARAMETER n= 29,m= 18 original value
*IE N 50 $-PARAMETER n= 149,m= 98
*IE N 100 $-PARAMETER n= 299,m=198
*IE N 500 $-PARAMETER n= 1499,m=998
*IE N 1000 $-PARAMETER n= 2999,m=1998
IE N 1500 $-PARAMETER n= 4499,m=2998
*IE N 5000 $-PARAMETER n=14999,m=9998
* Constants
IA N-1 N -1
IE 1 1
IE 2 2
RI RN N
RD S RN 1.0
RD 2/S S 2.0
RM -S S -1.0
VARIABLES
DO T 1 N-1
X X(T)
OD T
DO T 1 N
DO I 1 2
X Y(T,I)
OD I
OD T
GROUPS
* Objective function
DO T 1 N-1
ZN O(T) 'SCALE' 2/S
OD T
* Transition constraints
DO T 1 N-1
IA T+1 T 1
XE TT(T,1) Y(T+1,1) -1.0 Y(T,1) 1.0
ZE TT(T,1) Y(T,2) S
XE TT(T,2) Y(T+1,2) -1.0 Y(T,2) 1.0
ZE TT(T,2) Y(T,1) -S
ZE TT(T,2) X(T) S
OD T
BOUNDS
FR DTOC3 'DEFAULT'
XX DTOC3 Y(1,1) 15.0
XX DTOC3 Y(1,2) 5.0
START POINT
XV DTOC3 Y(1,1) 15.0
XV DTOC3 Y(1,2) 5.0
ELEMENT TYPE
EV SQ YY
ELEMENT USES
DO T 2 N
XT Y1SQ(T) SQ
ZV Y1SQ(T) YY Y(T,1)
XT Y2SQ(T) SQ
ZV Y2SQ(T) YY Y(T,2)
OD T
DO T 1 N-1
XT XSQ(T) SQ
ZV XSQ(T) YY X(T)
OD T
GROUP USES
DO T 1 N-1
IA T+1 T 1
XE O(T) Y1SQ(T+1) 2.0 Y2SQ(T+1) 1.0
XE O(T) XSQ(T) 6.0
OD T
OBJECT BOUND
LO DTOC3 0.0
*LO SOLUTION( 10) 224.590381002
*LO SOLUTION( 50) 233.278523083
*LO SOLUTION( 100) 234.286202920
*LO SOLUTION( 500) 235.084407947
*LO SOLUTION(1000) 235.182824435
*LO SOLUTION(5000) 235.154640099
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DTOC3
INDIVIDUALS
T SQ
F YY * YY
G YY YY + YY
H YY YY 2.0
ENDATA